Name: fermi estimation for physical quantities
Uploaded: 2023-05-16T08:18:41.000Z
Duration: 1 min 5 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physical Science

PS.1

PS.1.b

Estimation of the Physical Quantities

Los problemas que involucran la estimación de cantidades físicas a menudo se denominan problemas de Fermi, llamado así por el físico Enrico Fermi, quien es conocido por hacer estimaciones rápidas y aproximadas basadas en cálculos y suposiciones simples.
La determinación del número de briznas de hierba en un campo de fútbol es un ejemplo de un problema de Fermi.
La respuesta a cualquier problema de Fermi, llamada estimación de Fermi, se logra dividiendo el problema en partes más pequeñas y utilizando la información disponible para estimar aproximadamente las incógnitas.
Ahora, el número de briznas de césped en un campo de fútbol se puede estimar considerando las dimensiones del campo y estimando que hay 20 briznas de césped en un centímetro cuadrado.
A partir de la longitud y el ancho, se calcula el área del campo de fútbol.
A continuación, convirtiendo el área del campo en centímetros y multiplicando el área por el número de briznas de hierba por unidad de superficie, se obtiene la estimación de Fermi del número total de briznas de hierba.

<ol>
	<li>OpenStax. (2019). Física Universitaria Vol. 1. [Versión web]. Obtenido de <a href="https://openstax.org/books/university-physics-volume-1/pages/1-5-estimates-and-fermi-calculations">https://openstax.org/books/university-physics-volume-1/pages/1-5-estimates-and-fermi-calculations</a>, sección 1.5; páginas 25-27</li>
</ol>

estimación de las magnitudes físicas

En muchas ocasiones, los físicos, otros científicos e ingenieros necesitan hacer estimaciones de una magnitud en particular. Estas a veces se conocen como estimaciones aproximadas, cálculos de orden de magnitud, cálculos de sobre la marcha o cálculos de Fermi. El físico Enrico Fermi era famoso por su habilidad para estimar diversos tipos de datos con sorprendente precisión. Estimar no significa adivinar un número o una fórmula al azar. En cambio, la estimación significa utilizar experiencias previas y razonamiento físico sólido para tener una idea aproximada del valor de una magnitud. Al determinar una aproximación confiable generalmente se requiere la identificación de los principios físicos correctos y una buena suposición sobre las variables relevantes, por lo que la estimación es muy útil para desarrollar la intuición física. Las estimaciones también nos permiten realizar "comprobaciones de cordura" en cálculos o propuestas de políticas al ayudarnos a descartar ciertos escenarios o números irreales.

Muchas estimaciones se basan en fórmulas en las que las magnitudes de entrada solo se conocen con un nivel limitado de precisión. Para avanzar en la estimación, uno debe tener algunas ideas definidas sobre cómo pueden estar relacionadas las variables. Las siguientes estrategias podrían ayudar a practicar el arte de la estimación:

<ul> 

	<li>- Obtener longitudes grandes a partir de longitudes más pequeñas: al estimar longitudes, recuerda que cualquier cosa puede servir como regla. Imagina dividir algo grande en cosas más pequeñas, estimar la longitud de una de las cosas más pequeñas y multiplicar para obtener la longitud de la cosa grande.</li> 

	<li>- Obtener áreas y volúmenes a partir de longitudes: al tratar con el área o el volumen de un objeto complejo, introduce un modelo simple del objeto, como una esfera o una caja. Luego, estima las dimensiones lineales primero y utiliza las estimaciones para obtener el volumen o el área mediante fórmulas geométricas estándar.</li> 

	<li>- Obtener masas a partir de volúmenes y densidades: al estimar las masas de los objetos, puede ser útil estimar primero su volumen y luego estimar su masa a partir de una estimación aproximada de su densidad promedio.</li> 

	<li>- Si todo lo demás falla, establece límites: para magnitudes físicas completamente desconocidas, piensa en qué debe ser mayor y qué debe ser menor.</li> 

	<li>- Una cifra significativa está bien: no es necesario ir más allá de una cifra significativa o un dígito en el coeficiente de una expresión en notación científica al hacer cálculos para obtener una estimación.</li> 

	<li>- Pregunta lo siguiente: ¿Tiene sentido esto? Verifica si la respuesta es razonable. ¿Cómo se compara con los valores de otras magnitudes conocidas con las mismas dimensiones?</li>

</ul>

Estimación de las magnitudes Físicas

En muchas ocasiones, los físicos, otros científicos e ingenieros necesitan hacer estimaciones de una cantidad particular. A veces se denominan ...

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Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

Units, Dimensions, and Measurements

Unidades, dimensiones y mediciones

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

fermi estimation for physical quantities

Fermi estimation helps physicists, scientists, and engineers make rough calculations for physical quantities. These estimates are also called guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. Enrico Fermi was known for making these kinds of estimates with surprising precision.

Estimation is not random guessing. It uses prior experience and sound physical reasoning to get a rough value for a quantity. This kind of reasoning helps build physical intuition. It also gives a useful sanity check by showing when a result or policy idea seems unrealistic.

Many estimates start with formulas that use input values known only to limited precision. To move forward, it helps to decide how the variables are related. One way to estimate length is to break a large object into smaller parts. Another way is to remember that almost anything can serve as a ruler.

Area and volume estimates often begin with a simple model of the object. A sphere or a box can stand in for a more complex shape. Estimate the linear dimensions first, then use standard geometry formulas to find the area or volume. Mass estimates can then follow from volume and a rough average density.

If a quantity is hard to figure out, it is still useful to bound it. That means deciding what it must be bigger than and smaller than. When doing the math, one significant figure is usually enough. Afterward, check whether the answer makes sense and compare it with other known quantities that have the same dimensions.

Fermi Estimation for Physical Quantities

the scope of physics

How Physics Shapes Science and Technology

Physics studies the interactions of energy, matter, space, and time. It looks for the basic mechanisms that explain natural phenomena. The word physics comes from the Greek word physis, which means nature. Physics helps us understand the natural world at its most fundamental level. It relies on quantitative laws, or rules written in numbers and measurements, to describe how things behave. That approach can also help other fields improve the limits of current technology. Physics matters in...

orders of magnitude

Estimating Scale with Powers of 10

Orders of magnitude help estimate the scale of a number using powers of 10. It is a simple way to round values to the nearest power of 10. This makes it easier to compare very large and very small numbers. To find the order of magnitude of a number, take its base-10 logarithm and round to the nearest integer. The result gives the power of 10 that most closely matches the original value. This method gives a consistent estimate of size without using exact digits. Orders of magnitude are useful...

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models, theories, and laws

Scientific Models, Theories, and Laws

Scientific models, theories, and laws help physicists describe natural phenomena. A model is a simplified version of a physical system that is too complex to study in full. It acts as a rough mental or visual picture of what may be happening. Good models keep the important parts and simplify the rest so the problem becomes workable. The light wave model is one example. Light waves are usually invisible, so they cannot be seen in the same way as water waves. Even so, it is useful to think of...

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units and standards of measurement

SI Units for Physical Quantities

SI units give a standard way to measure physical quantities. A physical quantity can be defined by how it is measured or by how it is calculated from other measurements. For example, the mass and dimensions of a metallic cube can be found with a weighing machine and a meter scale. Some quantities are built from others. The volume of a cube is the cube of its side length. The density of the cube is then found by dividing mass by volume. Measurements are written in units, which are standardized...

estimation of the physical quantities

Fermi estimation helps physicists, scientists, and engineers make rough calculations for physical quantities. These estimates are also called guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. Enrico Fermi was known for making these kinds of estimates with surprising precision. Estimation is not random guessing. It uses prior experience and sound physical reasoning to get a rough value for a quantity. This kind of reasoning helps build...

base quantities and derived quantities

SI Base Units Behind Measured Quantities

SI base units are the starting point for measuring physical quantities. In any system of units, some quantities must be defined through direct measurement. These are called base quantities, and their units are base units. Other physical quantities are built from these base values by algebraic combinations. These are called derived quantities, and their units are derived units. For example, area comes from two lengths multiplied together. It is a derived quantity and is written in SI base units...

conversion of units

Unit Conversion Steps and Real-World Errors

Unit conversion lets you change a measurement from one unit to another. It is useful in everyday life, such as when a cookbook gives amounts in liters or ounces and you need cups instead. It also helps when directions use feet or meters, but you want to know the distance in miles. The first step is to list the given unit and the unit you need. The second step is to choose a conversion factor, which is a ratio that shows how many of one unit equal another unit. For example, 1,000 meters equal 1...

accuracy and precision

Repeated Measurements in Science

Repeated measurements help scientists check the quality of their results. They are used to judge both precision and accuracy. These two ideas are related, but they do not mean the same thing. Measurements are precise when repeated trials give very similar results. Precision shows how closely the values agree with one another. Measurements are accurate when the result is very close to the true value or the accepted value. Accuracy shows how closely the values agree with the real target. High...

random and systematic errors

How Measurement Errors Affect Results

Measurement errors can change how accurate and precise a result appears. Scientists try to record measurements as carefully as possible, but errors can still happen. These errors are usually random or systematic. Random errors come from inconsistency or fluctuation in the measuring process. They can also come from changes in the quantity being measured. In repeated measurements, random error may make a value appear greater than the true value one time and less than it the next. A simple...

rules for significant figures

Measurement Precision and Significant Figures

Measurement precision depends on the tool used, and significant figures show that precision. A ruler can measure length to the closest millimeter. A caliper can measure length to the nearest 0.01 mm, so it gives a more precise measurement because it can detect very small changes in length. When a value is written from a measurement, the last digit is not exact. The person making the measurement must estimate that digit. For example, a stick that seems to fall between 13.2 cm and 13.3 cm must...

significant figures in calculations

Rounding Rules for Significant Figures

Rounding rules for significant figures help show the right level of certainty in measured results. When a calculation is reported with the correct number of significant figures, it better matches the uncertainty in the measurements. The rounding rule depends on the type of math being done. For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places. For multiplication and division, the result should have the same number of...

dimensional analysis

Dimensional Checks in Physics Equations

Dimensional consistency is a key check in physics equations. It means the dimensions on both sides of an equation must match. The idea helps show whether an equation can represent a real physical law. The first rule is simple: expressions on each side of the equal sign must have the same dimensions. That makes sense because you can only add or subtract quantities of the same type. The second rule says that the input to a standard mathematical function, such as a trigonometric function, a...

problem solving: dimensional analysis

Dimensional Checks for Physics Equations

Dimensional analysis helps check whether physics equations make sense. It compares the dimensions on each side of an equation and shows whether the units are consistent. This method is useful for spotting algebra errors, typos, and for remembering physical laws. A valid equation must follow two rules. First, both sides of an equality must have the same dimension, so only quantities with matching dimensions can be added or subtracted. Second, common math functions such as exponential,...

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solving problems in physics

Physics Problem Solving: Strategy to Check

Physics problem solving uses general physical principles to work out specific situations. It is a key skill in physics, and it can also help with everyday life. The same analytical skills can be used in new situations, while a list of facts can never cover every possible case. Solving physics problems also takes creativity and insight. These skills grow with experience and practice. There is no simple step-by-step method that works for every problem, but a three-stage process can guide the...

key terms and concepts

Learn Fermi estimation for physical quantities using rough calculations, bounds, density, and sanity checks to build strong physics intuition.

Fermi Estimation for Physical Quantities | JoVE K12

physics

JoVE Core Física presenta la teoría y la aplicación de conceptos físicos fundamentales, como la cinemática, dinámica, mecánica de fluidos, estática, ondas y acústica, mediante animaciones audiovisuales concisas y fáciles de entender. Además, los vídeos de científicos en acción muestran la aplicación de los conceptos relacionados en experimentos de investigación clásicos y originales, realizados en laboratorios de todo el mundo.

PH.1

PH.1.b

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.1

CHEM.1.E

Specialised Topic in Science

112.51.c.1.

112.51.c.2.C.

PHYS.2

PHYS.2.A

PHYS.2.C

Chemistry and Physics

IPC.2

IPC.2.A

IPC.2.C

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PS.1.d

Fermi Estimation for Physical Quantities

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